Realization of topological Bragg and locally resonant interface states in one-dimensional metamaterial beam-resonator-foundation system

Abstract In this study, the one-dimensional (1D) metamaterial beam-foundation system is innovatively improved into a metamaterial beam-resonator-foundation system by inserting resonators into the elastic foundation for ultra-low frequency vibration attenuation and enhanced topological energy trapping. Abundant band gap characteristics are obtained including quasi-static band gap starting from 0 Hz, Bragg scattering band gaps (BSBGs), and local resonance band gaps (LRBGs). Five band folding points are obtained through the band folding mechanism which can be opened by tuning inner and outer resonance parameters. However, only three band folding induced band gaps support mode inversion and Zak phase transition, including one BSBG and two LRBGs. The topological inversion in LRBGs is rarely reported in the 1D mechanical system, which can induce topological locally resonant interface states. The underlying physical mechanism of the topological phase transition in LRBG is revealed, which results from the topological inversion band gap transition from an initial BSBG to a LRBG with resonance parameters changes. Different from conventional 1D topological metamaterials that merely utilize local resonance to lower the band frequency and achieve subwavelength topological states in BSBGs, the topological interface states in LRBGs can localize wave energy to fewer unit cells near the interface, exhibiting enhanced energy localization capacity. The topologically protected interface states are validated with defective cases, demonstrating the potential of topological metamaterials for robust energy harvesting. This study provides new insights into the topological theory of 1D mechanical systems and contributes to the development and implementation of multi-functional devices integrating vibration attenuation and energy trapping.